Question

suppose that you have a 10,000 in a rather risky investment recommend by your financial advisor during the first year your investment decreases by 50% of its original value during the second year your investment at the end of year 1 increases by 60%. Weiser tells you that there must have there must have been a 10% overall increase of your original $10,000 investment. Is your financial advisor using percentages Properly? If Not, what is your actual gain or loss of your original $10,000 investment?

Answer 1

The financial advisor is NOT using percentages properly, because the 60% increase would multiply the new value after one year, and not the initial value.

So first let's find the investment after one year:

$\begin{gathered} 10000-50\text{\% of 10000} \\ =10000-0.5\cdot10000=10000-5000=5000 \end{gathered}$

Then, we have an increase of 60%, so:

$\begin{gathered} 5000+60\text{\% of 5000} \\ =5000+0.6\cdot5000=5000+3000=8000 \end{gathered}$

The final value is 8000, which is lesser than the original value, so we have a loss.

The percentual loss is:

$\frac{10000-8000}{10000}=\frac{2000}{10000}=0.2=20\text{\%}$